To make a live event invite-only, you can require participants to enter a password on the join screen on their device.
Note, this is a feature available to upgraded accounts only.
How to enable event password protection
Select "Start an Event" top right corner
This will open the event settings modal
Click the toggle next to "Require password to join" at the bottom of the check boxes options (you will only be able to click this if you have a paid account)
Enter a password
Select Launch
You players' join screens will ask them for a password, see the join screen below
"Join At" URL reminder display
Adding a password will also automatically pre-close the "join at" event code notice in the top left corner of your live event. You can re-open this by clicking in the top left corner.